Properties

Label 585.2.dp.a.397.3
Level 585585
Weight 22
Character 585.397
Analytic conductor 4.6714.671
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [585,2,Mod(28,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 585=32513 585 = 3^{2} \cdot 5 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 585.dp (of order 1212, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.671248518244.67124851824
Analytic rank: 00
Dimension: 2020
Relative dimension: 55 over Q(ζ12)\Q(\zeta_{12})
Coefficient field: Q[x]/(x20+)\mathbb{Q}[x]/(x^{20} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20+26x18+279x16+1604x14+5353x12+10466x10+11441x8+6176x6++1 x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 397.3
Root 0.493902i0.493902i of defining polynomial
Character χ\chi == 585.397
Dual form 585.2.dp.a.28.3

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.427732+0.246951i)q2+(0.8780301.52079i)q4+(0.284413+2.21791i)q5+(1.83775+3.18307i)q71.85513iq8+(0.426062+1.01890i)q10+(0.177987+0.664257i)q11+(2.92331+2.11051i)q13+1.81533iq14+(1.29794+2.24809i)q16+(2.293590.614565i)q17+(5.29067+1.41763i)q19+(3.123252.37992i)q20+(0.0879082+0.328078i)q22+(1.30811+0.350507i)q23+(4.83822+1.26160i)q25+(1.77158+0.180816i)q26+(3.227195.58966i)q28+(8.24134+4.75814i)q29+(4.81595+4.81595i)q31+(4.32351+2.49618i)q32+(0.8292730.829273i)q34+(6.53707+4.98125i)q35+(0.917615+1.58936i)q37+(1.91290+1.91290i)q38+(4.114490.527621i)q40+(0.5349880.143350i)q41+(0.560778+2.09285i)q43+(0.8539190.853919i)q44+(0.6460780.173116i)q46+3.80918q47+(3.25462+5.63717i)q49+(2.381010.655176i)q50+(5.77640+2.59266i)q52+(2.472932.47293i)q53+(1.42264+0.583682i)q55+(5.904993.40925i)q56+(2.35005+4.07041i)q58+(2.6931010.0508i)q59+(3.099045.36770i)q61+(0.870630+3.24924i)q62+2.72601q64+(5.512345.88338i)q65+(10.60666.12371i)q67+(1.07921+4.02768i)q68+(4.02624+0.516303i)q70+(1.735006.47512i)q713.37642iq73+(0.784986+0.453212i)q74+(2.489459.29074i)q76+(1.78728+1.78728i)q77+3.12149iq79+(5.355212.23932i)q80+(0.264231+0.0708006i)q822.13918q83+(0.7107235.26175i)q85+(0.756694+0.756694i)q86+(1.232280.330188i)q88+(3.26255+0.874198i)q89+(12.09025.42653i)q91+(1.68161+1.68161i)q92+(1.62931+0.940681i)q94+(1.63944+12.1374i)q95+(6.126063.53688i)q97+(2.78421+1.60746i)q98+O(q100)q+(0.427732 + 0.246951i) q^{2} +(-0.878030 - 1.52079i) q^{4} +(0.284413 + 2.21791i) q^{5} +(1.83775 + 3.18307i) q^{7} -1.85513i q^{8} +(-0.426062 + 1.01890i) q^{10} +(0.177987 + 0.664257i) q^{11} +(-2.92331 + 2.11051i) q^{13} +1.81533i q^{14} +(-1.29794 + 2.24809i) q^{16} +(-2.29359 - 0.614565i) q^{17} +(5.29067 + 1.41763i) q^{19} +(3.12325 - 2.37992i) q^{20} +(-0.0879082 + 0.328078i) q^{22} +(-1.30811 + 0.350507i) q^{23} +(-4.83822 + 1.26160i) q^{25} +(-1.77158 + 0.180816i) q^{26} +(3.22719 - 5.58966i) q^{28} +(8.24134 + 4.75814i) q^{29} +(4.81595 + 4.81595i) q^{31} +(-4.32351 + 2.49618i) q^{32} +(-0.829273 - 0.829273i) q^{34} +(-6.53707 + 4.98125i) q^{35} +(-0.917615 + 1.58936i) q^{37} +(1.91290 + 1.91290i) q^{38} +(4.11449 - 0.527621i) q^{40} +(0.534988 - 0.143350i) q^{41} +(-0.560778 + 2.09285i) q^{43} +(0.853919 - 0.853919i) q^{44} +(-0.646078 - 0.173116i) q^{46} +3.80918 q^{47} +(-3.25462 + 5.63717i) q^{49} +(-2.38101 - 0.655176i) q^{50} +(5.77640 + 2.59266i) q^{52} +(2.47293 - 2.47293i) q^{53} +(-1.42264 + 0.583682i) q^{55} +(5.90499 - 3.40925i) q^{56} +(2.35005 + 4.07041i) q^{58} +(2.69310 - 10.0508i) q^{59} +(-3.09904 - 5.36770i) q^{61} +(0.870630 + 3.24924i) q^{62} +2.72601 q^{64} +(-5.51234 - 5.88338i) q^{65} +(-10.6066 - 6.12371i) q^{67} +(1.07921 + 4.02768i) q^{68} +(-4.02624 + 0.516303i) q^{70} +(1.73500 - 6.47512i) q^{71} -3.37642i q^{73} +(-0.784986 + 0.453212i) q^{74} +(-2.48945 - 9.29074i) q^{76} +(-1.78728 + 1.78728i) q^{77} +3.12149i q^{79} +(-5.35521 - 2.23932i) q^{80} +(0.264231 + 0.0708006i) q^{82} -2.13918 q^{83} +(0.710723 - 5.26175i) q^{85} +(-0.756694 + 0.756694i) q^{86} +(1.23228 - 0.330188i) q^{88} +(-3.26255 + 0.874198i) q^{89} +(-12.0902 - 5.42653i) q^{91} +(1.68161 + 1.68161i) q^{92} +(1.62931 + 0.940681i) q^{94} +(-1.63944 + 12.1374i) q^{95} +(6.12606 - 3.53688i) q^{97} +(-2.78421 + 1.60746i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+6q2+6q42q72q10+16q114q132q164q1720q19+16q22+10q23+18q25+24q26+18q2848q32+2q3440q354q37++30q98+O(q100) 20 q + 6 q^{2} + 6 q^{4} - 2 q^{7} - 2 q^{10} + 16 q^{11} - 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 16 q^{22} + 10 q^{23} + 18 q^{25} + 24 q^{26} + 18 q^{28} - 48 q^{32} + 2 q^{34} - 40 q^{35} - 4 q^{37}+ \cdots + 30 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/585Z)×\left(\mathbb{Z}/585\mathbb{Z}\right)^\times.

nn 326326 352352 496496
χ(n)\chi(n) 11 e(14)e\left(\frac{1}{4}\right) e(1112)e\left(\frac{11}{12}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.427732 + 0.246951i 0.302452 + 0.174621i 0.643544 0.765409i 0.277463π-0.277463\pi
−0.341092 + 0.940030i 0.610797π0.610797\pi
33 0 0
44 −0.878030 1.52079i −0.439015 0.760397i
55 0.284413 + 2.21791i 0.127193 + 0.991878i
66 0 0
77 1.83775 + 3.18307i 0.694603 + 1.20309i 0.970314 + 0.241847i 0.0777532π0.0777532\pi
−0.275712 + 0.961240i 0.588914π0.588914\pi
88 1.85513i 0.655886i
99 0 0
1010 −0.426062 + 1.01890i −0.134733 + 0.322206i
1111 0.177987 + 0.664257i 0.0536651 + 0.200281i 0.987553 0.157284i 0.0502738π-0.0502738\pi
−0.933888 + 0.357565i 0.883607π0.883607\pi
1212 0 0
1313 −2.92331 + 2.11051i −0.810781 + 0.585350i
1414 1.81533i 0.485168i
1515 0 0
1616 −1.29794 + 2.24809i −0.324484 + 0.562023i
1717 −2.29359 0.614565i −0.556277 0.149054i −0.0302815 0.999541i 0.509640π-0.509640\pi
−0.525995 + 0.850487i 0.676307π0.676307\pi
1818 0 0
1919 5.29067 + 1.41763i 1.21376 + 0.325227i 0.808238 0.588857i 0.200422π-0.200422\pi
0.405526 + 0.914084i 0.367088π0.367088\pi
2020 3.12325 2.37992i 0.698381 0.532167i
2121 0 0
2222 −0.0879082 + 0.328078i −0.0187421 + 0.0699464i
2323 −1.30811 + 0.350507i −0.272760 + 0.0730858i −0.392606 0.919707i 0.628426π-0.628426\pi
0.119846 + 0.992792i 0.461760π0.461760\pi
2424 0 0
2525 −4.83822 + 1.26160i −0.967644 + 0.252320i
2626 −1.77158 + 0.180816i −0.347436 + 0.0354610i
2727 0 0
2828 3.22719 5.58966i 0.609882 1.05635i
2929 8.24134 + 4.75814i 1.53038 + 0.883564i 0.999344 + 0.0362142i 0.0115299π0.0115299\pi
0.531034 + 0.847350i 0.321803π0.321803\pi
3030 0 0
3131 4.81595 + 4.81595i 0.864970 + 0.864970i 0.991910 0.126940i 0.0405157π-0.0405157\pi
−0.126940 + 0.991910i 0.540516π0.540516\pi
3232 −4.32351 + 2.49618i −0.764295 + 0.441266i
3333 0 0
3434 −0.829273 0.829273i −0.142219 0.142219i
3535 −6.53707 + 4.98125i −1.10497 + 0.841986i
3636 0 0
3737 −0.917615 + 1.58936i −0.150855 + 0.261289i −0.931542 0.363634i 0.881536π-0.881536\pi
0.780687 + 0.624922i 0.214869π0.214869\pi
3838 1.91290 + 1.91290i 0.310314 + 0.310314i
3939 0 0
4040 4.11449 0.527621i 0.650559 0.0834242i
4141 0.534988 0.143350i 0.0835510 0.0223874i −0.216801 0.976216i 0.569562π-0.569562\pi
0.300352 + 0.953828i 0.402896π0.402896\pi
4242 0 0
4343 −0.560778 + 2.09285i −0.0855178 + 0.319157i −0.995412 0.0956841i 0.969496π-0.969496\pi
0.909894 + 0.414841i 0.136163π0.136163\pi
4444 0.853919 0.853919i 0.128733 0.128733i
4545 0 0
4646 −0.646078 0.173116i −0.0952590 0.0255246i
4747 3.80918 0.555626 0.277813 0.960635i 0.410390π-0.410390\pi
0.277813 + 0.960635i 0.410390π0.410390\pi
4848 0 0
4949 −3.25462 + 5.63717i −0.464946 + 0.805310i
5050 −2.38101 0.655176i −0.336726 0.0926559i
5151 0 0
5252 5.77640 + 2.59266i 0.801043 + 0.359538i
5353 2.47293 2.47293i 0.339683 0.339683i −0.516565 0.856248i 0.672789π-0.672789\pi
0.856248 + 0.516565i 0.172789π0.172789\pi
5454 0 0
5555 −1.42264 + 0.583682i −0.191828 + 0.0787036i
5656 5.90499 3.40925i 0.789088 0.455580i
5757 0 0
5858 2.35005 + 4.07041i 0.308577 + 0.534471i
5959 2.69310 10.0508i 0.350612 1.30850i −0.535305 0.844659i 0.679803π-0.679803\pi
0.885917 0.463844i 0.153530π-0.153530\pi
6060 0 0
6161 −3.09904 5.36770i −0.396792 0.687263i 0.596536 0.802586i 0.296543π-0.296543\pi
−0.993328 + 0.115323i 0.963210π0.963210\pi
6262 0.870630 + 3.24924i 0.110570 + 0.412653i
6363 0 0
6464 2.72601 0.340751
6565 −5.51234 5.88338i −0.683721 0.729743i
6666 0 0
6767 −10.6066 6.12371i −1.29580 0.748130i −0.316124 0.948718i 0.602381π-0.602381\pi
−0.979676 + 0.200588i 0.935715π0.935715\pi
6868 1.07921 + 4.02768i 0.130874 + 0.488428i
6969 0 0
7070 −4.02624 + 0.516303i −0.481227 + 0.0617101i
7171 1.73500 6.47512i 0.205907 0.768456i −0.783264 0.621689i 0.786447π-0.786447\pi
0.989171 0.146767i 0.0468866π-0.0468866\pi
7272 0 0
7373 3.37642i 0.395180i −0.980285 0.197590i 0.936688π-0.936688\pi
0.980285 0.197590i 0.0633115π-0.0633115\pi
7474 −0.784986 + 0.453212i −0.0912528 + 0.0526848i
7575 0 0
7676 −2.48945 9.29074i −0.285559 1.06572i
7777 −1.78728 + 1.78728i −0.203680 + 0.203680i
7878 0 0
7979 3.12149i 0.351195i 0.984462 + 0.175598i 0.0561857π0.0561857\pi
−0.984462 + 0.175598i 0.943814π0.943814\pi
8080 −5.35521 2.23932i −0.598730 0.250363i
8181 0 0
8282 0.264231 + 0.0708006i 0.0291795 + 0.00781862i
8383 −2.13918 −0.234805 −0.117403 0.993084i 0.537457π-0.537457\pi
−0.117403 + 0.993084i 0.537457π0.537457\pi
8484 0 0
8585 0.710723 5.26175i 0.0770887 0.570717i
8686 −0.756694 + 0.756694i −0.0815964 + 0.0815964i
8787 0 0
8888 1.23228 0.330188i 0.131361 0.0351982i
8989 −3.26255 + 0.874198i −0.345830 + 0.0926648i −0.427553 0.903990i 0.640624π-0.640624\pi
0.0817233 + 0.996655i 0.473958π0.473958\pi
9090 0 0
9191 −12.0902 5.42653i −1.26740 0.568855i
9292 1.68161 + 1.68161i 0.175320 + 0.175320i
9393 0 0
9494 1.62931 + 0.940681i 0.168050 + 0.0970238i
9595 −1.63944 + 12.1374i −0.168203 + 1.24527i
9696 0 0
9797 6.12606 3.53688i 0.622007 0.359116i −0.155643 0.987813i 0.549745π-0.549745\pi
0.777650 + 0.628697i 0.216412π0.216412\pi
9898 −2.78421 + 1.60746i −0.281248 + 0.162378i
9999 0 0
100100 6.16674 + 6.25021i 0.616674 + 0.625021i
101101 −12.9641 7.48483i −1.28998 0.744769i −0.311327 0.950303i 0.600774π-0.600774\pi
−0.978650 + 0.205534i 0.934107π0.934107\pi
102102 0 0
103103 −3.17851 3.17851i −0.313188 0.313188i 0.532956 0.846143i 0.321081π-0.321081\pi
−0.846143 + 0.532956i 0.821081π0.821081\pi
104104 3.91526 + 5.42311i 0.383923 + 0.531780i
105105 0 0
106106 1.66844 0.447058i 0.162054 0.0434221i
107107 −14.7329 + 3.94767i −1.42428 + 0.381635i −0.887001 0.461767i 0.847216π-0.847216\pi
−0.537282 + 0.843403i 0.680549π0.680549\pi
108108 0 0
109109 2.25902 2.25902i 0.216375 0.216375i −0.590594 0.806969i 0.701107π-0.701107\pi
0.806969 + 0.590594i 0.201107π0.201107\pi
110110 −0.752648 0.101663i −0.0717622 0.00969315i
111111 0 0
112112 −9.54111 −0.901550
113113 16.0061 + 4.28882i 1.50573 + 0.403458i 0.915014 0.403423i 0.132180π-0.132180\pi
0.590713 + 0.806881i 0.298846π0.298846\pi
114114 0 0
115115 −1.14944 2.80158i −0.107185 0.261248i
116116 16.7112i 1.55159i
117117 0 0
118118 3.63398 3.63398i 0.334535 0.334535i
119119 −2.25883 8.43007i −0.207067 0.772783i
120120 0 0
121121 9.11672 5.26354i 0.828793 0.478504i
122122 3.06124i 0.277152i
123123 0 0
124124 3.09551 11.5526i 0.277985 1.03746i
125125 −4.17416 10.3719i −0.373349 0.927691i
126126 0 0
127127 −2.14812 8.01688i −0.190614 0.711383i −0.993359 0.115059i 0.963294π-0.963294\pi
0.802744 0.596324i 0.203372π-0.203372\pi
128128 9.81302 + 5.66555i 0.867356 + 0.500768i
129129 0 0
130130 −0.904895 3.87778i −0.0793645 0.340104i
131131 −1.37409 −0.120054 −0.0600272 0.998197i 0.519119π-0.519119\pi
−0.0600272 + 0.998197i 0.519119π0.519119\pi
132132 0 0
133133 5.21049 + 19.4458i 0.451807 + 1.68617i
134134 −3.02451 5.23861i −0.261278 0.452547i
135135 0 0
136136 −1.14010 + 4.25489i −0.0977624 + 0.364854i
137137 6.16380 + 10.6760i 0.526609 + 0.912114i 0.999519 + 0.0310029i 0.00987013π0.00987013\pi
−0.472910 + 0.881111i 0.656797π0.656797\pi
138138 0 0
139139 5.54392 3.20078i 0.470229 0.271487i −0.246107 0.969243i 0.579151π-0.579151\pi
0.716336 + 0.697756i 0.245818π0.245818\pi
140140 13.3152 + 5.56784i 1.12534 + 0.470569i
141141 0 0
142142 2.34115 2.34115i 0.196465 0.196465i
143143 −1.92223 1.56619i −0.160745 0.130971i
144144 0 0
145145 −8.20917 + 19.6318i −0.681734 + 1.63033i
146146 0.833811 1.44420i 0.0690067 0.119523i
147147 0 0
148148 3.22278 0.264911
149149 16.2300 + 4.34882i 1.32961 + 0.356269i 0.852571 0.522611i 0.175042π-0.175042\pi
0.477043 + 0.878880i 0.341709π0.341709\pi
150150 0 0
151151 −3.31542 + 3.31542i −0.269805 + 0.269805i −0.829022 0.559217i 0.811102π-0.811102\pi
0.559217 + 0.829022i 0.311102π0.311102\pi
152152 2.62988 9.81486i 0.213312 0.796090i
153153 0 0
154154 −1.20585 + 0.323106i −0.0971699 + 0.0260366i
155155 −9.31161 + 12.0510i −0.747926 + 0.967963i
156156 0 0
157157 9.87941 + 9.87941i 0.788463 + 0.788463i 0.981242 0.192779i 0.0617501π-0.0617501\pi
−0.192779 + 0.981242i 0.561750π0.561750\pi
158158 −0.770855 + 1.33516i −0.0613259 + 0.106220i
159159 0 0
160160 −6.76595 8.87919i −0.534895 0.701962i
161161 −3.51966 3.51966i −0.277388 0.277388i
162162 0 0
163163 −0.114289 + 0.0659848i −0.00895180 + 0.00516833i −0.504469 0.863430i 0.668312π-0.668312\pi
0.495517 + 0.868598i 0.334978π0.334978\pi
164164 −0.687741 0.687741i −0.0537035 0.0537035i
165165 0 0
166166 −0.914995 0.528272i −0.0710174 0.0410019i
167167 10.8184 18.7380i 0.837152 1.44999i −0.0551149 0.998480i 0.517553π-0.517553\pi
0.892267 0.451509i 0.149114π-0.149114\pi
168168 0 0
169169 4.09151 12.3393i 0.314731 0.949181i
170170 1.60339 2.07510i 0.122975 0.159153i
171171 0 0
172172 3.67518 0.984760i 0.280230 0.0750873i
173173 2.00162 7.47013i 0.152180 0.567943i −0.847150 0.531353i 0.821684π-0.821684\pi
0.999330 0.0365902i 0.0116496π-0.0116496\pi
174174 0 0
175175 −12.9072 13.0819i −0.975691 0.988898i
176176 −1.72433 0.462032i −0.129976 0.0348270i
177177 0 0
178178 −1.61138 0.431768i −0.120778 0.0323624i
179179 −8.17681 + 14.1627i −0.611164 + 1.05857i 0.379881 + 0.925035i 0.375965π0.375965\pi
−0.991045 + 0.133531i 0.957368π0.957368\pi
180180 0 0
181181 18.0387i 1.34081i −0.741997 0.670403i 0.766121π-0.766121\pi
0.741997 0.670403i 0.233879π-0.233879\pi
182182 −3.83127 5.30678i −0.283993 0.393365i
183183 0 0
184184 0.650235 + 2.42671i 0.0479359 + 0.178899i
185185 −3.78603 1.58315i −0.278354 0.116396i
186186 0 0
187187 1.63292i 0.119411i
188188 −3.34458 5.79298i −0.243928 0.422496i
189189 0 0
190190 −3.69858 + 4.78669i −0.268324 + 0.347263i
191191 2.59552 + 4.49557i 0.187805 + 0.325288i 0.944518 0.328459i 0.106529π-0.106529\pi
−0.756713 + 0.653747i 0.773196π0.773196\pi
192192 0 0
193193 −8.74813 5.05073i −0.629704 0.363560i 0.150934 0.988544i 0.451772π-0.451772\pi
−0.780637 + 0.624984i 0.785105π0.785105\pi
194194 3.49375 0.250836
195195 0 0
196196 11.4306 0.816473
197197 11.3137 + 6.53197i 0.806068 + 0.465384i 0.845589 0.533835i 0.179250π-0.179250\pi
−0.0395205 + 0.999219i 0.512583π0.512583\pi
198198 0 0
199199 −3.92506 6.79840i −0.278240 0.481926i 0.692707 0.721219i 0.256418π-0.256418\pi
−0.970947 + 0.239293i 0.923084π0.923084\pi
200200 2.34043 + 8.97550i 0.165493 + 0.634664i
201201 0 0
202202 −3.69677 6.40300i −0.260104 0.450513i
203203 34.9770i 2.45491i
204204 0 0
205205 0.470093 + 1.14578i 0.0328327 + 0.0800249i
206206 −0.574613 2.14448i −0.0400352 0.149413i
207207 0 0
208208 −0.950343 9.31118i −0.0658944 0.645614i
209209 3.76669i 0.260547i
210210 0 0
211211 −6.21205 + 10.7596i −0.427655 + 0.740720i −0.996664 0.0816108i 0.973994π-0.973994\pi
0.569009 + 0.822331i 0.307327π0.307327\pi
212212 −5.93213 1.58951i −0.407420 0.109168i
213213 0 0
214214 −7.27661 1.94976i −0.497419 0.133283i
215215 −4.80124 0.648520i −0.327442 0.0442287i
216216 0 0
217217 −6.47901 + 24.1800i −0.439824 + 1.64145i
218218 1.52412 0.408387i 0.103226 0.0276594i
219219 0 0
220220 2.13678 + 1.65105i 0.144062 + 0.111314i
221221 8.00192 3.04407i 0.538267 0.204766i
222222 0 0
223223 −4.97247 + 8.61258i −0.332981 + 0.576741i −0.983095 0.183096i 0.941388π-0.941388\pi
0.650114 + 0.759837i 0.274721π0.274721\pi
224224 −15.8910 9.17468i −1.06176 0.613009i
225225 0 0
226226 5.78718 + 5.78718i 0.384958 + 0.384958i
227227 −12.6490 + 7.30290i −0.839543 + 0.484710i −0.857109 0.515135i 0.827742π-0.827742\pi
0.0175659 + 0.999846i 0.494408π0.494408\pi
228228 0 0
229229 15.6183 + 15.6183i 1.03209 + 1.03209i 0.999468 + 0.0326207i 0.0103853π0.0103853\pi
0.0326207 + 0.999468i 0.489615π0.489615\pi
230230 0.200203 1.48218i 0.0132010 0.0977319i
231231 0 0
232232 8.82695 15.2887i 0.579517 1.00375i
233233 −16.5625 16.5625i −1.08505 1.08505i −0.996030 0.0890148i 0.971628π-0.971628\pi
−0.0890148 0.996030i 0.528372π-0.528372\pi
234234 0 0
235235 1.08338 + 8.44841i 0.0706719 + 0.551113i
236236 −17.6498 + 4.72926i −1.14891 + 0.307848i
237237 0 0
238238 1.11564 4.16362i 0.0723162 0.269888i
239239 14.6022 14.6022i 0.944535 0.944535i −0.0540053 0.998541i 0.517199π-0.517199\pi
0.998541 + 0.0540053i 0.0171988π0.0171988\pi
240240 0 0
241241 2.99335 + 0.802065i 0.192818 + 0.0516656i 0.353936 0.935270i 0.384843π-0.384843\pi
−0.161117 + 0.986935i 0.551510π0.551510\pi
242242 5.19935 0.334227
243243 0 0
244244 −5.44211 + 9.42600i −0.348395 + 0.603438i
245245 −13.4284 5.61516i −0.857907 0.358740i
246246 0 0
247247 −18.4582 + 7.02183i −1.17447 + 0.446788i
248248 8.93419 8.93419i 0.567322 0.567322i
249249 0 0
250250 0.775929 5.46720i 0.0490741 0.345776i
251251 25.5728 14.7645i 1.61414 0.931925i 0.625745 0.780028i 0.284795π-0.284795\pi
0.988396 0.151897i 0.0485382π-0.0485382\pi
252252 0 0
253253 −0.465654 0.806536i −0.0292754 0.0507065i
254254 1.06096 3.95955i 0.0665704 0.248444i
255255 0 0
256256 0.0722145 + 0.125079i 0.00451341 + 0.00781745i
257257 1.85447 + 6.92097i 0.115679 + 0.431718i 0.999337 0.0364143i 0.0115936π-0.0115936\pi
−0.883658 + 0.468133i 0.844927π0.844927\pi
258258 0 0
259259 −6.74538 −0.419137
260260 −4.10740 + 13.5489i −0.254730 + 0.840268i
261261 0 0
262262 −0.587740 0.339332i −0.0363107 0.0209640i
263263 3.48511 + 13.0066i 0.214901 + 0.802023i 0.986201 + 0.165551i 0.0529402π0.0529402\pi
−0.771300 + 0.636472i 0.780393π0.780393\pi
264264 0 0
265265 6.18807 + 4.78140i 0.380130 + 0.293719i
266266 −2.57347 + 9.60433i −0.157790 + 0.588879i
267267 0 0
268268 21.5072i 1.31376i
269269 7.01806 4.05188i 0.427899 0.247047i −0.270552 0.962705i 0.587206π-0.587206\pi
0.698451 + 0.715658i 0.253873π0.253873\pi
270270 0 0
271271 −2.38026 8.88325i −0.144590 0.539619i −0.999773 0.0212923i 0.993222π-0.993222\pi
0.855183 0.518326i 0.173445π-0.173445\pi
272272 4.35853 4.35853i 0.264275 0.264275i
273273 0 0
274274 6.08862i 0.367827i
275275 −1.69917 2.98927i −0.102464 0.180260i
276276 0 0
277277 24.9641 + 6.68911i 1.49995 + 0.401910i 0.913082 0.407775i 0.133695π-0.133695\pi
0.586865 + 0.809685i 0.300362π0.300362\pi
278278 3.16174 0.189629
279279 0 0
280280 9.24085 + 12.1271i 0.552246 + 0.724732i
281281 −5.41928 + 5.41928i −0.323287 + 0.323287i −0.850027 0.526740i 0.823414π-0.823414\pi
0.526740 + 0.850027i 0.323414π0.323414\pi
282282 0 0
283283 8.48623 2.27388i 0.504454 0.135168i 0.00238762 0.999997i 0.499240π-0.499240\pi
0.502066 + 0.864829i 0.332573π0.332573\pi
284284 −11.3707 + 3.04677i −0.674728 + 0.180793i
285285 0 0
286286 −0.435428 1.14460i −0.0257474 0.0676819i
287287 1.43946 + 1.43946i 0.0849688 + 0.0849688i
288288 0 0
289289 −9.83958 5.68088i −0.578799 0.334170i
290290 −8.35941 + 6.36988i −0.490882 + 0.374052i
291291 0 0
292292 −5.13484 + 2.96460i −0.300494 + 0.173490i
293293 −11.4627 + 6.61798i −0.669657 + 0.386626i −0.795947 0.605367i 0.793026π-0.793026\pi
0.126290 + 0.991993i 0.459693π0.459693\pi
294294 0 0
295295 23.0577 + 3.11448i 1.34247 + 0.181332i
296296 2.94846 + 1.70229i 0.171375 + 0.0989437i
297297 0 0
298298 5.86814 + 5.86814i 0.339932 + 0.339932i
299299 3.08427 3.78542i 0.178368 0.218916i
300300 0 0
301301 −7.69226 + 2.06114i −0.443375 + 0.118802i
302302 −2.23685 + 0.599363i −0.128716 + 0.0344895i
303303 0 0
304304 −10.0539 + 10.0539i −0.576632 + 0.576632i
305305 11.0236 8.40003i 0.631212 0.480984i
306306 0 0
307307 −15.4782 −0.883389 −0.441695 0.897165i 0.645623π-0.645623\pi
−0.441695 + 0.897165i 0.645623π0.645623\pi
308308 4.28737 + 1.14880i 0.244296 + 0.0654588i
309309 0 0
310310 −6.95889 + 2.85510i −0.395238 + 0.162159i
311311 5.34922i 0.303326i 0.988432 + 0.151663i 0.0484629π0.0484629\pi
−0.988432 + 0.151663i 0.951537π0.951537\pi
312312 0 0
313313 24.3923 24.3923i 1.37873 1.37873i 0.531967 0.846765i 0.321453π-0.321453\pi
0.846765 0.531967i 0.178547π-0.178547\pi
314314 1.78601 + 6.66547i 0.100790 + 0.376154i
315315 0 0
316316 4.74714 2.74076i 0.267048 0.154180i
317317 18.9851i 1.06631i 0.846017 + 0.533156i 0.178994π0.178994\pi
−0.846017 + 0.533156i 0.821006π0.821006\pi
318318 0 0
319319 −1.69378 + 6.32125i −0.0948332 + 0.353922i
320320 0.775312 + 6.04604i 0.0433412 + 0.337984i
321321 0 0
322322 −0.636287 2.37466i −0.0354589 0.132334i
323323 −11.2634 6.50293i −0.626712 0.361832i
324324 0 0
325325 11.4810 13.8992i 0.636852 0.770986i
326326 −0.0651800 −0.00360999
327327 0 0
328328 −0.265931 0.992469i −0.0146836 0.0548000i
329329 7.00031 + 12.1249i 0.385940 + 0.668467i
330330 0 0
331331 −1.81607 + 6.77766i −0.0998202 + 0.372534i −0.997706 0.0676941i 0.978436π-0.978436\pi
0.897886 + 0.440228i 0.145102π0.145102\pi
332332 1.87826 + 3.25325i 0.103083 + 0.178545i
333333 0 0
334334 9.25473 5.34322i 0.506396 0.292368i
335335 10.5652 25.2661i 0.577237 1.38043i
336336 0 0
337337 −1.10195 + 1.10195i −0.0600271 + 0.0600271i −0.736483 0.676456i 0.763515π-0.763515\pi
0.676456 + 0.736483i 0.263515π0.263515\pi
338338 4.79728 4.26753i 0.260938 0.232123i
339339 0 0
340340 −8.62608 + 3.53912i −0.467815 + 0.191936i
341341 −2.34185 + 4.05620i −0.126818 + 0.219656i
342342 0 0
343343 1.80378 0.0973947
344344 3.88250 + 1.04031i 0.209331 + 0.0560899i
345345 0 0
346346 2.70091 2.70091i 0.145202 0.145202i
347347 −6.68561 + 24.9510i −0.358902 + 1.33944i 0.516600 + 0.856227i 0.327197π0.327197\pi
−0.875502 + 0.483214i 0.839469π0.839469\pi
348348 0 0
349349 −9.07958 + 2.43287i −0.486019 + 0.130228i −0.493504 0.869744i 0.664284π-0.664284\pi
0.00748510 + 0.999972i 0.497617π0.497617\pi
350350 −2.29023 8.78298i −0.122418 0.469470i
351351 0 0
352352 −2.42763 2.42763i −0.129393 0.129393i
353353 −1.63274 + 2.82798i −0.0869017 + 0.150518i −0.906200 0.422849i 0.861030π-0.861030\pi
0.819298 + 0.573368i 0.194363π0.194363\pi
354354 0 0
355355 14.8547 + 2.00647i 0.788404 + 0.106492i
356356 4.19410 + 4.19410i 0.222287 + 0.222287i
357357 0 0
358358 −6.99496 + 4.03854i −0.369695 + 0.213444i
359359 −3.12090 3.12090i −0.164715 0.164715i 0.619937 0.784652i 0.287158π-0.287158\pi
−0.784652 + 0.619937i 0.787158π0.787158\pi
360360 0 0
361361 9.52706 + 5.50045i 0.501424 + 0.289497i
362362 4.45468 7.71573i 0.234133 0.405530i
363363 0 0
364364 2.36294 + 23.1514i 0.123852 + 1.21346i
365365 7.48859 0.960297i 0.391971 0.0502643i
366366 0 0
367367 −24.2349 + 6.49371i −1.26505 + 0.338969i −0.828132 0.560533i 0.810596π-0.810596\pi
−0.436917 + 0.899502i 0.643930π0.643930\pi
368368 0.909872 3.39569i 0.0474303 0.177012i
369369 0 0
370370 −1.22844 1.61213i −0.0638636 0.0838105i
371371 12.4161 + 3.32690i 0.644614 + 0.172724i
372372 0 0
373373 11.0372 + 2.95740i 0.571483 + 0.153128i 0.532976 0.846130i 0.321073π-0.321073\pi
0.0385061 + 0.999258i 0.487740π0.487740\pi
374374 0.403250 0.698450i 0.0208516 0.0361160i
375375 0 0
376376 7.06651i 0.364427i
377377 −34.1341 + 3.48389i −1.75800 + 0.179429i
378378 0 0
379379 0.520109 + 1.94107i 0.0267162 + 0.0997062i 0.977997 0.208621i 0.0668975π-0.0668975\pi
−0.951280 + 0.308327i 0.900231π0.900231\pi
380380 19.8980 8.16377i 1.02074 0.418792i
381381 0 0
382382 2.56386i 0.131179i
383383 −13.2258 22.9077i −0.675806 1.17053i −0.976233 0.216725i 0.930462π-0.930462\pi
0.300427 0.953805i 0.402871π-0.402871\pi
384384 0 0
385385 −4.47235 3.45570i −0.227932 0.176119i
386386 −2.49457 4.32072i −0.126970 0.219919i
387387 0 0
388388 −10.7577 6.21098i −0.546141 0.315315i
389389 0.650094 0.0329611 0.0164805 0.999864i 0.494754π-0.494754\pi
0.0164805 + 0.999864i 0.494754π0.494754\pi
390390 0 0
391391 3.21568 0.162624
392392 10.4577 + 6.03773i 0.528191 + 0.304951i
393393 0 0
394394 3.22615 + 5.58786i 0.162531 + 0.281512i
395395 −6.92317 + 0.887791i −0.348343 + 0.0446696i
396396 0 0
397397 13.5041 + 23.3897i 0.677750 + 1.17390i 0.975657 + 0.219303i 0.0703782π0.0703782\pi
−0.297907 + 0.954595i 0.596288π0.596288\pi
398398 3.87719i 0.194346i
399399 0 0
400400 3.44350 12.5142i 0.172175 0.625712i
401401 1.28339 + 4.78969i 0.0640896 + 0.239186i 0.990539 0.137235i 0.0438215π-0.0438215\pi
−0.926449 + 0.376421i 0.877155π0.877155\pi
402402 0 0
403403 −24.2426 3.91442i −1.20761 0.194991i
404404 26.2876i 1.30786i
405405 0 0
406406 −8.63761 + 14.9608i −0.428677 + 0.742491i
407407 −1.21906 0.326647i −0.0604268 0.0161913i
408408 0 0
409409 5.83965 + 1.56473i 0.288752 + 0.0773708i 0.400288 0.916390i 0.368910π-0.368910\pi
−0.111536 + 0.993760i 0.535577π0.535577\pi
410410 −0.0818784 + 0.606177i −0.00404368 + 0.0299370i
411411 0 0
412412 −2.04303 + 7.62468i −0.100653 + 0.375641i
413413 36.9416 9.89848i 1.81778 0.487073i
414414 0 0
415415 −0.608410 4.74450i −0.0298657 0.232898i
416416 7.37076 16.4219i 0.361381 0.805150i
417417 0 0
418418 −0.930187 + 1.61113i −0.0454969 + 0.0788030i
419419 −4.65114 2.68534i −0.227223 0.131187i 0.382067 0.924135i 0.375212π-0.375212\pi
−0.609290 + 0.792947i 0.708546π0.708546\pi
420420 0 0
421421 14.1377 + 14.1377i 0.689029 + 0.689029i 0.962017 0.272988i 0.0880119π-0.0880119\pi
−0.272988 + 0.962017i 0.588012π0.588012\pi
422422 −5.31418 + 3.06814i −0.258690 + 0.149355i
423423 0 0
424424 −4.58760 4.58760i −0.222794 0.222794i
425425 11.8722 + 0.0798070i 0.575887 + 0.00387121i
426426 0 0
427427 11.3905 19.7289i 0.551225 0.954750i
428428 18.9395 + 18.9395i 0.915476 + 0.915476i
429429 0 0
430430 −1.89349 1.46306i −0.0913122 0.0705552i
431431 −16.1219 + 4.31985i −0.776564 + 0.208080i −0.625269 0.780409i 0.715011π-0.715011\pi
−0.151295 + 0.988489i 0.548344π0.548344\pi
432432 0 0
433433 −1.96538 + 7.33490i −0.0944502 + 0.352493i −0.996936 0.0782277i 0.975074π-0.975074\pi
0.902485 + 0.430721i 0.141741π0.141741\pi
434434 −8.74255 + 8.74255i −0.419656 + 0.419656i
435435 0 0
436436 −5.41899 1.45201i −0.259522 0.0695388i
437437 −7.41767 −0.354835
438438 0 0
439439 6.84536 11.8565i 0.326711 0.565880i −0.655146 0.755502i 0.727393π-0.727393\pi
0.981857 + 0.189622i 0.0607262π0.0607262\pi
440440 1.08280 + 2.63917i 0.0516206 + 0.125818i
441441 0 0
442442 4.17441 + 0.674036i 0.198556 + 0.0320606i
443443 −6.46290 + 6.46290i −0.307062 + 0.307062i −0.843769 0.536707i 0.819668π-0.819668\pi
0.536707 + 0.843769i 0.319668π0.319668\pi
444444 0 0
445445 −2.86680 6.98740i −0.135899 0.331235i
446446 −4.25377 + 2.45591i −0.201422 + 0.116291i
447447 0 0
448448 5.00971 + 8.67708i 0.236687 + 0.409953i
449449 6.65458 24.8352i 0.314049 1.17205i −0.610822 0.791768i 0.709161π-0.709161\pi
0.924872 0.380280i 0.124172π-0.124172\pi
450450 0 0
451451 0.190442 + 0.329855i 0.00896755 + 0.0155323i
452452 −7.53143 28.1077i −0.354249 1.32207i
453453 0 0
454454 −7.21383 −0.338562
455455 8.59693 28.3583i 0.403030 1.32946i
456456 0 0
457457 −0.716665 0.413767i −0.0335242 0.0193552i 0.483144 0.875541i 0.339495π-0.339495\pi
−0.516668 + 0.856186i 0.672828π0.672828\pi
458458 2.82349 + 10.5374i 0.131933 + 0.492381i
459459 0 0
460460 −3.25138 + 4.20792i −0.151596 + 0.196195i
461461 −6.23219 + 23.2589i −0.290262 + 1.08327i 0.654646 + 0.755936i 0.272818π0.272818\pi
−0.944908 + 0.327337i 0.893849π0.893849\pi
462462 0 0
463463 6.35566i 0.295373i −0.989034 0.147686i 0.952817π-0.952817\pi
0.989034 0.147686i 0.0471826π-0.0471826\pi
464464 −21.3935 + 12.3515i −0.993167 + 0.573405i
465465 0 0
466466 −2.99418 11.1744i −0.138703 0.517645i
467467 15.6194 15.6194i 0.722781 0.722781i −0.246390 0.969171i 0.579244π-0.579244\pi
0.969171 + 0.246390i 0.0792443π0.0792443\pi
468468 0 0
469469 45.0153i 2.07861i
470470 −1.62295 + 3.88119i −0.0748610 + 0.179026i
471471 0 0
472472 −18.6455 4.99605i −0.858229 0.229962i
473473 −1.49000 −0.0685104
474474 0 0
475475 −27.3859 0.184093i −1.25655 0.00844675i
476476 −10.8371 + 10.8371i −0.496716 + 0.496716i
477477 0 0
478478 9.85182 2.63979i 0.450612 0.120741i
479479 −9.14111 + 2.44935i −0.417668 + 0.111914i −0.461532 0.887124i 0.652700π-0.652700\pi
0.0438638 + 0.999038i 0.486033π0.486033\pi
480480 0 0
481481 −0.671874 6.58282i −0.0306348 0.300151i
482482 1.08228 + 1.08228i 0.0492964 + 0.0492964i
483483 0 0
484484 −16.0095 9.24310i −0.727705 0.420141i
485485 9.58681 + 12.5811i 0.435314 + 0.571278i
486486 0 0
487487 5.33382 3.07948i 0.241698 0.139545i −0.374259 0.927324i 0.622103π-0.622103\pi
0.615957 + 0.787780i 0.288769π0.288769\pi
488488 −9.95775 + 5.74911i −0.450766 + 0.260250i
489489 0 0
490490 −4.35707 5.71793i −0.196832 0.258310i
491491 −12.8290 7.40681i −0.578964 0.334265i 0.181758 0.983343i 0.441821π-0.441821\pi
−0.760721 + 0.649078i 0.775155π0.775155\pi
492492 0 0
493493 −15.9781 15.9781i −0.719615 0.719615i
494494 −9.62921 1.55481i −0.433238 0.0699544i
495495 0 0
496496 −17.0775 + 4.57590i −0.766802 + 0.205464i
497497 23.7993 6.37699i 1.06754 0.286047i
498498 0 0
499499 21.0529 21.0529i 0.942459 0.942459i −0.0559733 0.998432i 0.517826π-0.517826\pi
0.998432 + 0.0559733i 0.0178262π0.0178262\pi
500500 −12.1085 + 15.4549i −0.541508 + 0.691164i
501501 0 0
502502 14.5844 0.650933
503503 −37.4393 10.0318i −1.66934 0.447297i −0.704404 0.709799i 0.748786π-0.748786\pi
−0.964932 + 0.262502i 0.915452π0.915452\pi
504504 0 0
505505 12.9135 30.8820i 0.574643 1.37423i
506506 0.459974i 0.0204484i
507507 0 0
508508 −10.3059 + 10.3059i −0.457250 + 0.457250i
509509 1.43699 + 5.36291i 0.0636933 + 0.237707i 0.990432 0.137999i 0.0440670π-0.0440670\pi
−0.926739 + 0.375706i 0.877400π0.877400\pi
510510 0 0
511511 10.7474 6.20501i 0.475437 0.274493i
512512 22.5909i 0.998384i
513513 0 0
514514 −0.915926 + 3.41828i −0.0403997 + 0.150774i
515515 6.14563 7.95364i 0.270809 0.350479i
516516 0 0
517517 0.677985 + 2.53028i 0.0298178 + 0.111281i
518518 −2.88521 1.66578i −0.126769 0.0731900i
519519 0 0
520520 −10.9144 + 10.2261i −0.478628 + 0.448443i
521521 13.8692 0.607619 0.303809 0.952733i 0.401741π-0.401741\pi
0.303809 + 0.952733i 0.401741π0.401741\pi
522522 0 0
523523 8.10818 + 30.2601i 0.354546 + 1.32318i 0.881055 + 0.473014i 0.156834π0.156834\pi
−0.526509 + 0.850170i 0.676499π0.676499\pi
524524 1.20649 + 2.08970i 0.0527057 + 0.0912890i
525525 0 0
526526 −1.72130 + 6.42400i −0.0750524 + 0.280100i
527527 −8.08609 14.0055i −0.352236 0.610090i
528528 0 0
529529 −18.3303 + 10.5830i −0.796969 + 0.460130i
530530 1.46606 + 3.57331i 0.0636816 + 0.155214i
531531 0 0
532532 24.9981 24.9981i 1.08381 1.08381i
533533 −1.26140 + 1.54815i −0.0546371 + 0.0670579i
534534 0 0
535535 −12.9458 31.5534i −0.559695 1.36417i
536536 −11.3602 + 19.6765i −0.490688 + 0.849897i
537537 0 0
538538 4.00246 0.172558
539539 −4.32381 1.15856i −0.186240 0.0499028i
540540 0 0
541541 −10.7732 + 10.7732i −0.463175 + 0.463175i −0.899695 0.436520i 0.856211π-0.856211\pi
0.436520 + 0.899695i 0.356211π0.356211\pi
542542 1.17561 4.38745i 0.0504969 0.188457i
543543 0 0
544544 11.4504 3.06813i 0.490932 0.131545i
545545 5.65278 + 4.36780i 0.242139 + 0.187096i
546546 0 0
547547 14.2704 + 14.2704i 0.610159 + 0.610159i 0.942987 0.332828i 0.108003π-0.108003\pi
−0.332828 + 0.942987i 0.608003π0.608003\pi
548548 10.8240 18.7477i 0.462379 0.800863i
549549 0 0
550550 0.0114157 1.69822i 0.000486767 0.0724122i
551551 36.8569 + 36.8569i 1.57016 + 1.57016i
552552 0 0
553553 −9.93592 + 5.73651i −0.422518 + 0.243941i
554554 9.02605 + 9.02605i 0.383480 + 0.383480i
555555 0 0
556556 −9.73546 5.62077i −0.412875 0.238374i
557557 8.35584 14.4727i 0.354048 0.613229i −0.632906 0.774228i 0.718138π-0.718138\pi
0.986955 + 0.160999i 0.0514716π0.0514716\pi
558558 0 0
559559 −2.77765 7.30159i −0.117482 0.308824i
560560 −2.71361 21.1613i −0.114671 0.894227i
561561 0 0
562562 −3.65629 + 0.979701i −0.154231 + 0.0413262i
563563 5.84179 21.8019i 0.246202 0.918839i −0.726573 0.687089i 0.758888π-0.758888\pi
0.972775 0.231750i 0.0744452π-0.0744452\pi
564564 0 0
565565 −4.95987 + 36.7198i −0.208663 + 1.54481i
566566 4.19136 + 1.12307i 0.176176 + 0.0472063i
567567 0 0
568568 −12.0122 3.21865i −0.504019 0.135052i
569569 −2.86843 + 4.96826i −0.120251 + 0.208280i −0.919866 0.392232i 0.871703π-0.871703\pi
0.799616 + 0.600512i 0.205037π0.205037\pi
570570 0 0
571571 46.5634i 1.94862i 0.225214 + 0.974309i 0.427692π0.427692\pi
−0.225214 + 0.974309i 0.572308π0.572308\pi
572572 −0.694069 + 4.29848i −0.0290205 + 0.179728i
573573 0 0
574574 0.260227 + 0.971181i 0.0108617 + 0.0405363i
575575 5.88672 3.34614i 0.245493 0.139544i
576576 0 0
577577 28.9429i 1.20491i −0.798153 0.602455i 0.794189π-0.794189\pi
0.798153 0.602455i 0.205811π-0.205811\pi
578578 −2.80580 4.85978i −0.116706 0.202140i
579579 0 0
580580 37.0638 4.75287i 1.53899 0.197352i
581581 −3.93127 6.80916i −0.163097 0.282491i
582582 0 0
583583 2.08281 + 1.20251i 0.0862613 + 0.0498030i
584584 −6.26369 −0.259193
585585 0 0
586586 −6.53726 −0.270052
587587 −17.0534 9.84577i −0.703868 0.406379i 0.104918 0.994481i 0.466542π-0.466542\pi
−0.808787 + 0.588102i 0.799875π0.799875\pi
588588 0 0
589589 18.6524 + 32.3069i 0.768558 + 1.33118i
590590 9.09338 + 7.02628i 0.374368 + 0.289267i
591591 0 0
592592 −2.38201 4.12577i −0.0979001 0.169568i
593593 21.8216i 0.896106i −0.894007 0.448053i 0.852118π-0.852118\pi
0.894007 0.448053i 0.147882π-0.147882\pi
594594 0 0
595595 18.0547 7.40749i 0.740169 0.303677i
596596 −7.63679 28.5009i −0.312815 1.16744i
597597 0 0
598598 2.25405 0.857481i 0.0921750 0.0350650i
599599 37.6041i 1.53646i −0.640172 0.768232i 0.721137π-0.721137\pi
0.640172 0.768232i 0.278863π-0.278863\pi
600600 0 0
601601 10.1487 17.5781i 0.413976 0.717027i −0.581344 0.813658i 0.697473π-0.697473\pi
0.995320 + 0.0966302i 0.0308064π0.0308064\pi
602602 −3.79922 1.01800i −0.154845 0.0414905i
603603 0 0
604604 7.95310 + 2.13103i 0.323607 + 0.0867103i
605605 14.2670 + 18.7230i 0.580034 + 0.761199i
606606 0 0
607607 8.91757 33.2808i 0.361953 1.35083i −0.509552 0.860440i 0.670189π-0.670189\pi
0.871505 0.490387i 0.163144π-0.163144\pi
608608 −26.4129 + 7.07732i −1.07119 + 0.287023i
609609 0 0
610610 6.78955 0.870657i 0.274901 0.0352519i
611611 −11.1354 + 8.03931i −0.450491 + 0.325236i
612612 0 0
613613 12.4332 21.5350i 0.502173 0.869790i −0.497824 0.867278i 0.665867π-0.665867\pi
0.999997 0.00251133i 0.000799381π-0.000799381\pi
614614 −6.62053 3.82236i −0.267183 0.154258i
615615 0 0
616616 3.31563 + 3.31563i 0.133591 + 0.133591i
617617 24.0895 13.9081i 0.969805 0.559917i 0.0706286 0.997503i 0.477499π-0.477499\pi
0.899177 + 0.437585i 0.144166π0.144166\pi
618618 0 0
619619 −19.5593 19.5593i −0.786156 0.786156i 0.194705 0.980862i 0.437625π-0.437625\pi
−0.980862 + 0.194705i 0.937625π0.937625\pi
620620 26.5030 + 3.57985i 1.06439 + 0.143770i
621621 0 0
622622 −1.32099 + 2.28803i −0.0529671 + 0.0917416i
623623 −8.77838 8.77838i −0.351698 0.351698i
624624 0 0
625625 21.8167 12.2078i 0.872669 0.488312i
626626 16.4570 4.40965i 0.657755 0.176245i
627627 0 0
628628 6.35012 23.6990i 0.253397 0.945692i
629629 3.08139 3.08139i 0.122863 0.122863i
630630 0 0
631631 12.6187 + 3.38116i 0.502341 + 0.134602i 0.501086 0.865397i 0.332934π-0.332934\pi
0.00125496 + 0.999999i 0.499601π0.499601\pi
632632 5.79076 0.230344
633633 0 0
634634 −4.68840 + 8.12054i −0.186200 + 0.322508i
635635 17.1697 7.04442i 0.681360 0.279549i
636636 0 0
637637 −2.38302 23.3481i −0.0944186 0.925086i
638638 −2.28552 + 2.28552i −0.0904846 + 0.0904846i
639639 0 0
640640 −9.77471 + 23.3757i −0.386379 + 0.924006i
641641 −23.7092 + 13.6885i −0.936456 + 0.540663i −0.888848 0.458203i 0.848493π-0.848493\pi
−0.0476083 + 0.998866i 0.515160π0.515160\pi
642642 0 0
643643 −15.7510 27.2816i −0.621161 1.07588i −0.989270 0.146099i 0.953328π-0.953328\pi
0.368109 0.929783i 0.380005π-0.380005\pi
644644 −2.26231 + 8.44305i −0.0891475 + 0.332703i
645645 0 0
646646 −3.21181 5.56301i −0.126367 0.218874i
647647 10.8106 + 40.3457i 0.425008 + 1.58615i 0.763905 + 0.645329i 0.223280π0.223280\pi
−0.338896 + 0.940824i 0.610054π0.610054\pi
648648 0 0
649649 7.15565 0.280884
650650 8.34320 3.10986i 0.327247 0.121979i
651651 0 0
652652 0.200698 + 0.115873i 0.00785996 + 0.00453795i
653653 3.93069 + 14.6695i 0.153820 + 0.574064i 0.999204 + 0.0399041i 0.0127052π0.0127052\pi
−0.845384 + 0.534160i 0.820628π0.820628\pi
654654 0 0
655655 −0.390807 3.04759i −0.0152701 0.119079i
656656 −0.372117 + 1.38876i −0.0145287 + 0.0542220i
657657 0 0
658658 6.91493i 0.269572i
659659 24.6914 14.2556i 0.961840 0.555319i 0.0651015 0.997879i 0.479263π-0.479263\pi
0.896739 + 0.442560i 0.145930π0.145930\pi
660660 0 0
661661 −1.63091 6.08664i −0.0634351 0.236743i 0.926928 0.375240i 0.122440π-0.122440\pi
−0.990363 + 0.138497i 0.955773π0.955773\pi
662662 −2.45054 + 2.45054i −0.0952430 + 0.0952430i
663663 0 0
664664 3.96845i 0.154006i
665665 −41.6471 + 17.0870i −1.61501 + 0.662606i
666666 0 0
667667 −12.4483 3.33552i −0.482002 0.129152i
668668 −37.9955 −1.47009
669669 0 0
670670 10.7585 8.19801i 0.415638 0.316717i
671671 3.01394 3.01394i 0.116352 0.116352i
672672 0 0
673673 −22.1285 + 5.92931i −0.852991 + 0.228558i −0.658719 0.752389i 0.728901π-0.728901\pi
−0.194272 + 0.980948i 0.562235π0.562235\pi
674674 −0.743468 + 0.199212i −0.0286373 + 0.00767334i
675675 0 0
676676 −22.3581 + 4.61199i −0.859926 + 0.177384i
677677 16.1247 + 16.1247i 0.619724 + 0.619724i 0.945461 0.325736i 0.105612π-0.105612\pi
−0.325736 + 0.945461i 0.605612π0.605612\pi
678678 0 0
679679 22.5163 + 12.9998i 0.864096 + 0.498886i
680680 −9.76121 1.31848i −0.374325 0.0505614i
681681 0 0
682682 −2.00337 + 1.15664i −0.0767129 + 0.0442902i
683683 −27.7544 + 16.0240i −1.06199 + 0.613142i −0.925983 0.377565i 0.876761π-0.876761\pi
−0.136010 + 0.990707i 0.543428π0.543428\pi
684684 0 0
685685 −21.9253 + 16.7071i −0.837724 + 0.638346i
686686 0.771532 + 0.445444i 0.0294572 + 0.0170071i
687687 0 0
688688 −3.97707 3.97707i −0.151624 0.151624i
689689 −2.01001 + 12.4483i −0.0765753 + 0.474243i
690690 0 0
691691 −0.532264 + 0.142620i −0.0202483 + 0.00542551i −0.268929 0.963160i 0.586670π-0.586670\pi
0.248681 + 0.968586i 0.420003π0.420003\pi
692692 −13.1180 + 3.51496i −0.498672 + 0.133619i
693693 0 0
694694 −9.02132 + 9.02132i −0.342445 + 0.342445i
695695 8.67580 + 11.3855i 0.329092 + 0.431878i
696696 0 0
697697 −1.31514 −0.0498144
698698 −4.48442 1.20160i −0.169738 0.0454811i
699699 0 0
700700 −8.56194 + 31.1155i −0.323611 + 1.17605i
701701 9.52279i 0.359671i 0.983697 + 0.179835i 0.0575565π0.0575565\pi
−0.983697 + 0.179835i 0.942443π0.942443\pi
702702 0 0
703703 −7.10792 + 7.10792i −0.268080 + 0.268080i
704704 0.485195 + 1.81077i 0.0182865 + 0.0682460i
705705 0 0
706706 −1.39674 + 0.806411i −0.0525672 + 0.0303497i
707707 55.0209i 2.06927i
708708 0 0
709709 8.39944 31.3471i 0.315448 1.17727i −0.608124 0.793842i 0.708078π-0.708078\pi
0.923572 0.383425i 0.125255π-0.125255\pi
710710 5.85831 + 4.52661i 0.219859 + 0.169881i
711711 0 0
712712 1.62175 + 6.05244i 0.0607776 + 0.226825i
713713 −7.98782 4.61177i −0.299146 0.172712i
714714 0 0
715715 2.92695 4.70877i 0.109462 0.176098i
716716 28.7180 1.07324
717717 0 0
718718 −0.564197 2.10561i −0.0210557 0.0785808i
719719 −4.21240 7.29608i −0.157096 0.272098i 0.776724 0.629841i 0.216880π-0.216880\pi
−0.933820 + 0.357743i 0.883546π0.883546\pi
720720 0 0
721721 4.27612 15.9587i 0.159251 0.594333i
722722 2.71668 + 4.70543i 0.101104 + 0.175118i
723723 0 0
724724 −27.4332 + 15.8385i −1.01955 + 0.588635i
725725 −45.8763 12.6236i −1.70380 0.468830i
726726 0 0
727727 −8.33682 + 8.33682i −0.309195 + 0.309195i −0.844597 0.535402i 0.820160π-0.820160\pi
0.535402 + 0.844597i 0.320160π0.320160\pi
728728 −10.0669 + 22.4288i −0.373104 + 0.831268i
729729 0 0
730730 3.44025 + 1.43857i 0.127329 + 0.0532437i
731731 2.57239 4.45551i 0.0951432 0.164793i
732732 0 0
733733 −18.6238 −0.687887 −0.343944 0.938990i 0.611763π-0.611763\pi
−0.343944 + 0.938990i 0.611763π0.611763\pi
734734 −11.9696 3.20725i −0.441807 0.118382i
735735 0 0
736736 4.78070 4.78070i 0.176219 0.176219i
737737 2.17988 8.13543i 0.0802970 0.299672i
738738 0 0
739739 −31.8740 + 8.54061i −1.17250 + 0.314171i −0.791949 0.610587i 0.790934π-0.790934\pi
−0.380555 + 0.924758i 0.624267π0.624267\pi
740740 0.916598 + 7.14782i 0.0336948 + 0.262759i
741741 0 0
742742 4.48920 + 4.48920i 0.164804 + 0.164804i
743743 18.7850 32.5366i 0.689155 1.19365i −0.282957 0.959133i 0.591315π-0.591315\pi
0.972112 0.234518i 0.0753512π-0.0753512\pi
744744 0 0
745745 −5.02925 + 37.2335i −0.184258 + 1.36413i
746746 3.99061 + 3.99061i 0.146107 + 0.146107i
747747 0 0
748748 −2.48333 + 1.43375i −0.0907995 + 0.0524231i
749749 −39.6410 39.6410i −1.44845 1.44845i
750750 0 0
751751 −29.1051 16.8038i −1.06206 0.613181i −0.136059 0.990701i 0.543444π-0.543444\pi
−0.926001 + 0.377520i 0.876777π0.876777\pi
752752 −4.94407 + 8.56339i −0.180292 + 0.312275i
753753 0 0
754754 −15.4606 6.93928i −0.563041 0.252714i
755755 −8.29623 6.41034i −0.301931 0.233296i
756756 0 0
757757 15.5871 4.17654i 0.566521 0.151799i 0.0358205 0.999358i 0.488596π-0.488596\pi
0.530701 + 0.847559i 0.321929π0.321929\pi
758758 −0.256883 + 0.958699i −0.00933040 + 0.0348215i
759759 0 0
760760 22.5164 + 3.04137i 0.816756 + 0.110322i
761761 15.1340 + 4.05514i 0.548606 + 0.146999i 0.522467 0.852660i 0.325012π-0.325012\pi
0.0261397 + 0.999658i 0.491679π0.491679\pi
762762 0 0
763763 11.3421 + 3.03911i 0.410612 + 0.110023i
764764 4.55789 7.89449i 0.164899 0.285613i
765765 0 0
766766 13.0645i 0.472039i
767767 13.3395 + 35.0655i 0.481662 + 1.26614i
768768 0 0
769769 8.43930 + 31.4959i 0.304329 + 1.13577i 0.933522 + 0.358521i 0.116719π0.116719\pi
−0.629193 + 0.777249i 0.716614π0.716614\pi
770770 −1.05958 2.58256i −0.0381845 0.0930690i
771771 0 0
772772 17.7388i 0.638433i
773773 11.9531 + 20.7033i 0.429921 + 0.744646i 0.996866 0.0791103i 0.0252079π-0.0252079\pi
−0.566944 + 0.823756i 0.691875π0.691875\pi
774774 0 0
775775 −29.3764 17.2248i −1.05523 0.618733i
776776 −6.56136 11.3646i −0.235539 0.407966i
777777 0 0
778778 0.278066 + 0.160541i 0.00996914 + 0.00575569i
779779 3.03366 0.108692
780780 0 0
781781 4.60995 0.164957
782782 1.37545 + 0.794114i 0.0491858 + 0.0283975i
783783 0 0
784784 −8.44858 14.6334i −0.301735 0.522620i
785785 −19.1018 + 24.7214i −0.681772 + 0.882346i
786786 0 0
787787 −7.85572 13.6065i −0.280026 0.485020i 0.691365 0.722506i 0.257010π-0.257010\pi
−0.971391 + 0.237486i 0.923676π0.923676\pi
788788 22.9411i 0.817242i
789789 0 0
790790 −3.18050 1.32995i −0.113157 0.0473174i
791791 15.7635 + 58.8303i 0.560487 + 2.09176i
792792 0 0
793793 20.3880 + 9.15090i 0.724000 + 0.324958i
794794 13.3394i 0.473397i
795795 0 0
796796 −6.89264 + 11.9384i −0.244303 + 0.423146i
797797 30.1666 + 8.08312i 1.06856 + 0.286319i 0.749900 0.661552i 0.230102π-0.230102\pi
0.318656 + 0.947870i 0.396768π0.396768\pi
798798 0 0
799799 −8.73669 2.34099i −0.309082 0.0828183i
800800 17.7689 17.5316i 0.628225 0.619836i
801801 0 0
802802 −0.633871 + 2.36564i −0.0223827 + 0.0835336i
803803 2.24281 0.600960i 0.0791471 0.0212074i
804804 0 0
805805 6.80525 8.80732i 0.239853 0.310417i
806806 −9.40267 7.66106i −0.331195 0.269849i
807807 0 0
808808 −13.8853 + 24.0500i −0.488483 + 0.846078i
809809 −11.4546 6.61331i −0.402722 0.232512i 0.284936 0.958547i 0.408028π-0.408028\pi
−0.687658 + 0.726035i 0.741361π0.741361\pi
810810 0 0
811811 22.0736 + 22.0736i 0.775109 + 0.775109i 0.978995 0.203886i 0.0653572π-0.0653572\pi
−0.203886 + 0.978995i 0.565357π0.565357\pi
812812 53.1928 30.7109i 1.86670 1.07774i
813813 0 0
814814 −0.440767 0.440767i −0.0154489 0.0154489i
815815 −0.178853 0.234715i −0.00626496 0.00822172i
816816 0 0
817817 −5.93379 + 10.2776i −0.207597 + 0.359568i
818818 2.11139 + 2.11139i 0.0738230 + 0.0738230i
819819 0 0
820820 1.32974 1.72095i 0.0464366 0.0600981i
821821 8.74860 2.34418i 0.305328 0.0818124i −0.102902 0.994692i 0.532813π-0.532813\pi
0.408230 + 0.912879i 0.366146π0.366146\pi
822822 0 0
823823 10.8551 40.5117i 0.378384 1.41215i −0.469953 0.882691i 0.655729π-0.655729\pi
0.848337 0.529457i 0.177604π-0.177604\pi
824824 −5.89653 + 5.89653i −0.205415 + 0.205415i
825825 0 0
826826 18.2455 + 4.88888i 0.634844 + 0.170106i
827827 −38.2009 −1.32838 −0.664188 0.747566i 0.731222π-0.731222\pi
−0.664188 + 0.747566i 0.731222π0.731222\pi
828828 0 0
829829 −14.6750 + 25.4178i −0.509682 + 0.882796i 0.490255 + 0.871579i 0.336904π0.336904\pi
−0.999937 + 0.0112165i 0.996430π0.996430\pi
830830 0.911423 2.17962i 0.0316359 0.0756557i
831831 0 0
832832 −7.96898 + 5.75327i −0.276275 + 0.199459i
833833 10.9292 10.9292i 0.378673 0.378673i
834834 0 0
835835 44.6360 + 18.6648i 1.54469 + 0.645923i
836836 5.72835 3.30726i 0.198119 0.114384i
837837 0 0
838838 −1.32629 2.29721i −0.0458161 0.0793557i
839839 −9.11914 + 34.0331i −0.314828 + 1.17495i 0.609322 + 0.792923i 0.291442π0.291442\pi
−0.924150 + 0.382030i 0.875225π0.875225\pi
840840 0 0
841841 30.7798 + 53.3122i 1.06137 + 1.83835i
842842 2.55582 + 9.53846i 0.0880795 + 0.328717i
843843 0 0
844844 21.8175 0.750988
845845 28.5312 + 5.56512i 0.981503 + 0.191446i
846846 0 0
847847 33.5084 + 19.3461i 1.15136 + 0.664740i
848848 2.34967 + 8.76909i 0.0806880 + 0.301132i
849849 0 0
850850 5.05841 + 2.96599i 0.173502 + 0.101733i
851851 0.643261 2.40068i 0.0220507 0.0822944i
852852 0 0
853853 17.6392i 0.603954i −0.953315 0.301977i 0.902353π-0.902353\pi
0.953315 0.301977i 0.0976465π-0.0976465\pi
854854 9.74415 5.62579i 0.333438 0.192511i
855855 0 0
856856 7.32342 + 27.3314i 0.250309 + 0.934167i
857857 −6.30427 + 6.30427i −0.215350 + 0.215350i −0.806535 0.591186i 0.798660π-0.798660\pi
0.591186 + 0.806535i 0.298660π0.298660\pi
858858 0 0
859859 29.2307i 0.997338i 0.866793 + 0.498669i 0.166178π0.166178\pi
−0.866793 + 0.498669i 0.833822π0.833822\pi
860860 3.22937 + 7.87112i 0.110121 + 0.268403i
861861 0 0
862862 −7.96263 2.13358i −0.271208 0.0726701i
863863 15.7688 0.536775 0.268387 0.963311i 0.413509π-0.413509\pi
0.268387 + 0.963311i 0.413509π0.413509\pi
864864 0 0
865865 17.1373 + 2.31480i 0.582687 + 0.0787054i
866866 −2.65202 + 2.65202i −0.0901192 + 0.0901192i
867867 0 0
868868 42.4615 11.3775i 1.44124 0.386179i
869869 −2.07347 + 0.555585i −0.0703377 + 0.0188469i
870870 0 0
871871 43.9305 4.48375i 1.48853 0.151926i
872872 −4.19076 4.19076i −0.141917 0.141917i
873873 0 0
874874 −3.17277 1.83180i −0.107321 0.0619616i
875875 25.3434 32.3476i 0.856764 1.09355i
876876 0 0
877877 −38.7309 + 22.3613i −1.30785 + 0.755088i −0.981737 0.190242i 0.939073π-0.939073\pi
−0.326114 + 0.945331i 0.605739π0.605739\pi
878878 5.85595 3.38094i 0.197629 0.114101i
879879 0 0
880880 0.534323 3.95580i 0.0180120 0.133350i
881881 18.0323 + 10.4110i 0.607525 + 0.350755i 0.771996 0.635627i 0.219258π-0.219258\pi
−0.164471 + 0.986382i 0.552592π0.552592\pi
882882 0 0
883883 5.33747 + 5.33747i 0.179620 + 0.179620i 0.791190 0.611570i 0.209462π-0.209462\pi
−0.611570 + 0.791190i 0.709462π0.709462\pi
884884 −11.6553 9.49648i −0.392011 0.319401i
885885 0 0
886886 −4.36041 + 1.16837i −0.146491 + 0.0392521i
887887 −25.8911 + 6.93749i −0.869337 + 0.232938i −0.665801 0.746129i 0.731910π-0.731910\pi
−0.203536 + 0.979067i 0.565243π0.565243\pi
888888 0 0
889889 21.5706 21.5706i 0.723454 0.723454i
890890 0.499324 3.69669i 0.0167374 0.123913i
891891 0 0
892892 17.4639 0.584736
893893 20.1531 + 5.40002i 0.674399 + 0.180705i
894894 0 0
895895 −33.7370 14.1074i −1.12770 0.471557i
896896 41.6474i 1.39134i
897897 0 0
898898 8.97946 8.97946i 0.299648 0.299648i
899899 16.7749 + 62.6048i 0.559475 + 2.08799i
900900 0 0
901901 −7.19167 + 4.15211i −0.239589 + 0.138327i
902902 0.188119i 0.00626368i
903903 0 0
904904 7.95630 29.6933i 0.264623 0.987585i
905905 40.0082 5.13044i 1.32992 0.170542i
906906 0 0
907907 10.4931 + 39.1608i 0.348418 + 1.30031i 0.888568 + 0.458744i 0.151701π0.151701\pi
−0.540151 + 0.841568i 0.681633π0.681633\pi
908908 22.2124 + 12.8243i 0.737144 + 0.425590i
909909 0 0
910910 10.6803 10.0067i 0.354048 0.331720i
911911 −8.00072 −0.265076 −0.132538 0.991178i 0.542313π-0.542313\pi
−0.132538 + 0.991178i 0.542313π0.542313\pi
912912 0 0
913913 −0.380746 1.42096i −0.0126009 0.0470271i
914914 −0.204360 0.353962i −0.00675963 0.0117080i
915915 0 0
916916 10.0389 37.4656i 0.331694 1.23790i
917917 −2.52522 4.37381i −0.0833901 0.144436i
918918 0 0
919919 −1.84237 + 1.06369i −0.0607741 + 0.0350879i −0.530079 0.847948i 0.677838π-0.677838\pi
0.469305 + 0.883036i 0.344504π0.344504\pi
920920 −5.19728 + 2.13235i −0.171349 + 0.0703014i
921921 0 0
922922 −8.40950 + 8.40950i −0.276952 + 0.276952i
923923 8.59384 + 22.5905i 0.282870 + 0.743577i
924924 0 0
925925 2.43449 8.84732i 0.0800455 0.290898i
926926 1.56954 2.71852i 0.0515782 0.0893360i
927927 0 0
928928 −47.5087 −1.55955
929929 −19.2515 5.15841i −0.631620 0.169242i −0.0712153 0.997461i 0.522688π-0.522688\pi
−0.560405 + 0.828219i 0.689354π0.689354\pi
930930 0 0
931931 −25.2106 + 25.2106i −0.826243 + 0.826243i
932932 −10.6458 + 39.7305i −0.348713 + 1.30142i
933933 0 0
934934 10.5382 2.82369i 0.344819 0.0923940i
935935 3.62166 0.464422i 0.118441 0.0151882i
936936 0 0
937937 17.2774 + 17.2774i 0.564427 + 0.564427i 0.930562 0.366135i 0.119319π-0.119319\pi
−0.366135 + 0.930562i 0.619319π0.619319\pi
938938 11.1166 19.2545i 0.362969 0.628680i
939939 0 0
940940 11.8970 9.06556i 0.388039 0.295686i
941941 −24.2129 24.2129i −0.789319 0.789319i 0.192063 0.981383i 0.438482π-0.438482\pi
−0.981383 + 0.192063i 0.938482π0.938482\pi
942942 0 0
943943 −0.649578 + 0.375034i −0.0211532 + 0.0122128i
944944 19.0996 + 19.0996i 0.621640 + 0.621640i
945945 0 0
946946 −0.637321 0.367957i −0.0207211 0.0119633i
947947 −4.15045 + 7.18880i −0.134872 + 0.233605i −0.925548 0.378629i 0.876396π-0.876396\pi
0.790677 + 0.612234i 0.209729π0.209729\pi
948948 0 0
949949 7.12597 + 9.87034i 0.231319 + 0.320405i
950950 −11.6684 6.84172i −0.378572 0.221975i
951951 0 0
952952 −15.6388 + 4.19041i −0.506857 + 0.135812i
953953 −1.23858 + 4.62244i −0.0401215 + 0.149736i −0.983081 0.183173i 0.941363π-0.941363\pi
0.942959 + 0.332908i 0.108030π0.108030\pi
954954 0 0
955955 −9.23255 + 7.03521i −0.298758 + 0.227654i
956956 −35.0280 9.38573i −1.13289 0.303556i
957957 0 0
958958 −4.51481 1.20974i −0.145867 0.0390849i
959959 −22.6550 + 39.2396i −0.731568 + 1.26711i
960960 0 0
961961 15.3867i 0.496346i
962962 1.33825 2.98160i 0.0431470 0.0961306i
963963 0 0
964964 −1.40848 5.25650i −0.0453639 0.169301i
965965 8.71398 20.8390i 0.280513 0.670832i
966966 0 0
967967 8.78782i 0.282597i 0.989967 + 0.141299i 0.0451278π0.0451278\pi
−0.989967 + 0.141299i 0.954872π0.954872\pi
968968 −9.76453 16.9127i −0.313844 0.543594i
969969 0 0
970970 0.993666 + 7.74880i 0.0319047 + 0.248799i
971971 −2.71693 4.70586i −0.0871905 0.151018i 0.819132 0.573605i 0.194456π-0.194456\pi
−0.906323 + 0.422587i 0.861122π0.861122\pi
972972 0 0
973973 20.3766 + 11.7645i 0.653245 + 0.377151i
974974 3.04192 0.0974695
975975 0 0
976976 16.0894 0.515010
977977 −16.1709 9.33626i −0.517352 0.298693i 0.218499 0.975837i 0.429884π-0.429884\pi
−0.735851 + 0.677144i 0.763217π0.763217\pi
978978 0 0
979979 −1.16138 2.01158i −0.0371180 0.0642903i
980980 3.25101 + 25.3521i 0.103850 + 0.809842i
981981 0 0
982982 −3.65824 6.33626i −0.116739 0.202198i
983983 6.62470i 0.211295i 0.994404 + 0.105648i 0.0336915π0.0336915\pi
−0.994404 + 0.105648i 0.966308π0.966308\pi
984984 0 0
985985 −11.2695 + 26.9505i −0.359077 + 0.858715i
986986 −2.88852 10.7801i −0.0919893 0.343309i
987987 0 0
988988 26.8856 + 21.9057i 0.855346 + 0.696915i
989989 2.93424i 0.0933033i
990990 0 0
991991 21.6135 37.4357i 0.686576 1.18919i −0.286362 0.958121i 0.592446π-0.592446\pi
0.972939 0.231064i 0.0742206π-0.0742206\pi
992992 −32.8433 8.80033i −1.04277 0.279411i
993993 0 0
994994 11.7545 + 3.14961i 0.372830 + 0.0998995i
995995 13.9619 10.6390i 0.442621 0.337278i
996996 0 0
997997 11.7001 43.6654i 0.370547 1.38290i −0.489197 0.872173i 0.662710π-0.662710\pi
0.859744 0.510725i 0.170623π-0.170623\pi
998998 14.2040 3.80596i 0.449621 0.120476i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 585.2.dp.a.397.3 20
3.2 odd 2 65.2.t.a.7.3 yes 20
5.3 odd 4 585.2.cf.a.163.3 20
13.2 odd 12 585.2.cf.a.262.3 20
15.2 even 4 325.2.s.b.293.3 20
15.8 even 4 65.2.o.a.33.3 yes 20
15.14 odd 2 325.2.x.b.7.3 20
39.2 even 12 65.2.o.a.2.3 20
39.5 even 4 845.2.o.e.357.3 20
39.8 even 4 845.2.o.f.357.3 20
39.11 even 12 845.2.o.g.587.3 20
39.17 odd 6 845.2.f.d.437.5 20
39.20 even 12 845.2.k.d.577.5 20
39.23 odd 6 845.2.t.e.427.3 20
39.29 odd 6 845.2.t.f.427.3 20
39.32 even 12 845.2.k.e.577.6 20
39.35 odd 6 845.2.f.e.437.6 20
39.38 odd 2 845.2.t.g.657.3 20
65.28 even 12 inner 585.2.dp.a.28.3 20
195.2 odd 12 325.2.x.b.93.3 20
195.8 odd 4 845.2.t.e.188.3 20
195.23 even 12 845.2.o.f.258.3 20
195.38 even 4 845.2.o.g.488.3 20
195.68 even 12 845.2.o.e.258.3 20
195.83 odd 4 845.2.t.f.188.3 20
195.98 odd 12 845.2.f.d.408.6 20
195.113 even 12 845.2.k.e.268.6 20
195.119 even 12 325.2.s.b.132.3 20
195.128 odd 12 845.2.t.g.418.3 20
195.158 odd 12 65.2.t.a.28.3 yes 20
195.173 even 12 845.2.k.d.268.5 20
195.188 odd 12 845.2.f.e.408.5 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.o.a.2.3 20 39.2 even 12
65.2.o.a.33.3 yes 20 15.8 even 4
65.2.t.a.7.3 yes 20 3.2 odd 2
65.2.t.a.28.3 yes 20 195.158 odd 12
325.2.s.b.132.3 20 195.119 even 12
325.2.s.b.293.3 20 15.2 even 4
325.2.x.b.7.3 20 15.14 odd 2
325.2.x.b.93.3 20 195.2 odd 12
585.2.cf.a.163.3 20 5.3 odd 4
585.2.cf.a.262.3 20 13.2 odd 12
585.2.dp.a.28.3 20 65.28 even 12 inner
585.2.dp.a.397.3 20 1.1 even 1 trivial
845.2.f.d.408.6 20 195.98 odd 12
845.2.f.d.437.5 20 39.17 odd 6
845.2.f.e.408.5 20 195.188 odd 12
845.2.f.e.437.6 20 39.35 odd 6
845.2.k.d.268.5 20 195.173 even 12
845.2.k.d.577.5 20 39.20 even 12
845.2.k.e.268.6 20 195.113 even 12
845.2.k.e.577.6 20 39.32 even 12
845.2.o.e.258.3 20 195.68 even 12
845.2.o.e.357.3 20 39.5 even 4
845.2.o.f.258.3 20 195.23 even 12
845.2.o.f.357.3 20 39.8 even 4
845.2.o.g.488.3 20 195.38 even 4
845.2.o.g.587.3 20 39.11 even 12
845.2.t.e.188.3 20 195.8 odd 4
845.2.t.e.427.3 20 39.23 odd 6
845.2.t.f.188.3 20 195.83 odd 4
845.2.t.f.427.3 20 39.29 odd 6
845.2.t.g.418.3 20 195.128 odd 12
845.2.t.g.657.3 20 39.38 odd 2